Interplex modulation is a technique for combining three or more signals to generate a constant envelope composite signal. A constant envelope composite signal is desirable, because it allows a highly efficient power amplifier to be utilized.
As an example, for three signals, S1, S2, and S3, Interplex modulation allows combining these signals into a phase modulated composite signal that produces a constant envelope, thereby allowing the use of a high power amplifier without signal distortion. Taking these three signals, S1, S2, and S3, an Interplex modulator generates a composite signal that includes three desired components plus an unwanted cross-product
Signals generated by Interplex modulation are single-carrier, double sideband signals, which have a serious shortcoming and restriction. It is often desired to generate, amplify, and transmit spread-spectrum signals having multiple carriers, with each carrier modulated by one or more spreading codes.
A general form of an N-channel Interplex signal is as follows:
                              z          ⁡                      (            t            )                          =                                            2              ⁢                              P                s                                              ⁢                      sin            [                                                            ω                  o                                ⁢                t                            +                                                θ                  1                                ⁢                                                      s                    1                                    ⁡                                      (                    t                    )                                                              +                                                ∑                                      n                    =                    2                                    N                                ⁢                                                      θ                    n                                    ⁢                                                            s                      1                                        ⁡                                          (                      t                      )                                                        ⁢                                                            s                      n                                        ⁡                                          (                      t                      )                                                                                            ]                                              (        1        )            
where Ps is the signal power; sn(t)=dn(t)sq(ωnt)=±1 are modulating signals, with dn(t) being the data and sq(ωnt) being a periodic square waveform. Modulation indices θn determine the power allocated to each signal (or code), the power allocated to the RF carrier, and the power allocated (as a disadvantage) to cross modulation.
When N=3, for example, equation (1) may be rewritten as follows:z(t)=√{square root over (2Ps)}sin[ωct+θ1s1(t)+θ2s1(t)s2(t)+θ3s1(t)s3(t)]  (2)
The modulation indices θ2 and θ3 may be set to values that optimize data power efficiency, such as
      θ    2    =            θ      3        =                  π        4            .      Index θ1 may then be set to
  -      π    2  in order to suppress the carrier. Equation (2) then becomes:z(t)=√{square root over (Ps)}[s2(t)+s3(t)]sin ωct+√{square root over (Ps)}[s1(t)−s1(t)s2(t)s3(t)]cos ωct  (3)
The arrangement of the modulating (or code) signals in equation (3) is such that[s2(t)+s3(t)]2+[s1(t)−s1(t)s2(t)s3(t)]2=const  (4)and[s2(t)+s3(t)][s1(t)−s1(t)s2(t)s3(t)]=0  (5)Consequently, the signal z(t) has a constant envelope. Inspection of equations (4) and (5) reveals that a constant envelope may be achieved by cancelling the appropriate terms, which is made possible by the introduction of the cross modulation term s1(t)s2(t)s3(t) in equation (3).
It will be understood, from Equation (1) that the Interplex method is applicable to single-carrier signals only. In U.S. patent application Ser. No. 11/067,148, filed on Feb. 25, 2005, by Goran Djuknic, et al., the Interplex method is extended to multiple carrier signals, each of which may be modulated (or spread) by multiple code signals. As described therein, the composite signal includes N carriers with the following form:
                              z          ⁡                      (            t            )                          =                                            2              ⁢                              P                s                                              ⁢                                    ∑                              i                =                1                            N                        ⁢                                                            CC                  i                                ⁡                                  (                  t                  )                                            ⁢              cos              ⁢                                                          ⁢              2              ⁢                                                          ⁢                              π                ⁡                                  (                                                            f                      o                                        +                                          f                      i                                                        )                                            ⁢              t                                                          (        6        )            
Amplitudes CCi(t) are combinations of codes that modulate (or spread) the carriers at frequencies fo+fi. Constancy of the envelope of the signal z(t) from equation (6) is assured, if the amplitudes satisfy the following conditions:
                              Condition          ⁢                                          ⁢          1          ⁢                      :                          ⁢                                  ⁢                                            ∑                              i                =                1                            N                        ⁢                                          CC                i                2                            ⁡                              (                t                )                                              =          const                                    (        7        )                                          Condition          ⁢                                          ⁢          2          ⁢                      :                          ⁢                                  ⁢                                                            CC                i                            ⁡                              (                t                )                                      ⁢                                          CC                j                            ⁡                              (                t                )                                              =                      {                                                                                const                    ,                                                                                        i                    =                    j                                                                                                                    0                    ,                                                                                        i                    ≠                    j                                                                                                                      
These conditions are met within any chip interval, kTc≦t<(k+1)Tc, for k=0, 1, 2 . . . . The Tc is the common chip duration of codes constituting CCi(t)'s. If codes in CCi(t) use different chipping rates, then Tc is the duration of the shortest chip interval.
The conditions of equation (7) do not restrict placement of any number of code signals, in any combination, on any of the carrier frequencies. These conditions, based on a desired combination of spreading codes, just determine the type and number of additional cross-product terms necessary for canceling appropriate terms in order to provide a constant-envelope modulated signal.
The price paid for obtaining constant signal envelope is the generation of cross modulation terms, e.g. the terms s1(t)s2(t)s3(t) in Equation 3. These signals cannot be used by ordinary receivers in a constructive manner, and the power efficiency of the method is, therefore, reduced. The constancy of the modulated signal envelope may be achieved for any number of modulating signals, but that power efficiency quickly deteriorates with the number of signals combined. The same is true for both the original, single-carrier Interplex and the multicarrier method shown in equation (6).
A variation of the method described above may be obtained when both in-phase and quadrature components of multiple carriers are used to accommodate PRN codes. In general, for N carriers, the resulting composite signal has the following form:
                              s          ⁡                      (            t            )                          =                                            2              ⁢                              P                s                                              ⁢                                    ∑                              i                =                1                            N                        ⁢                          [                                                                                          CCI                      i                                        ⁡                                          (                      t                      )                                                        ⁢                                      cos                    ⁡                                          (                                                                        ω                          o                                                +                                                  ω                          i                                                                    )                                                        ⁢                  t                                +                                                                            CCQ                      i                                        ⁡                                          (                      t                      )                                                        ⁢                                      sin                    ⁡                                          (                                                                        ω                          o                                                +                                                  ω                          i                                                                    )                                                        ⁢                  t                                            ]                                                          (                  7          ⁢          a                )            where CCI(t) and CCQ(t) are PRN (pseudo random noise) code combinations for spreading the in-phase and quadrature carrier components, respectively. The CCI(t) and CCQ(t), in addition to containing pure codes, in general, also contain terms that are products of pure codes (these are usually called cross-products.)
The multi-carrier composite signal of equation (7a) has a constant envelope if the following two conditions are met:
                                                        ∑                              i                =                1                            N                        ⁢                          [                                                                    CCI                    i                    2                                    ⁡                                      (                    t                    )                                                  +                                                      CCQ                    i                    2                                    ⁡                                      (                    t                    )                                                              ]                                =          const                ⁢                                  ⁢        and                            (                  7          ⁢          b                )                                                                                                      CCI                  i                                ⁡                                  (                  t                  )                                            ⁢                                                CCI                  j                                ⁡                                  (                  t                  )                                                      +                                                            CCQ                  i                                ⁡                                  (                  t                  )                                            ⁢                                                CCQ                  j                                ⁡                                  (                  t                  )                                                              =          0                ⁢                                  ⁢                                                                              CCI                  j                                ⁡                                  (                  t                  )                                            ⁢                                                CCQ                  i                                ⁡                                  (                  t                  )                                                      -                                                            CCI                  i                                ⁡                                  (                  t                  )                                            ⁢                                                CCQ                  j                                ⁡                                  (                  t                  )                                                              =          0                ⁢                                  ⁢                  (                                    i              =              1                        ,            …            ⁢                                                  ,                          N              ;                                                          ⁢                              j                =                1                                      ,            …            ⁢                                                  ,                          N              ;                                                          ⁢                              i                ≠                j                                              )                                    (                  7          ⁢          c                )            The conditions are satisfied within any chip interval, kTc≦t<(k+1)Tc, for k=0, 1, 2, . . . ,. The Tc is the common chip duration of codes that constitute code combinations is CCIi(t) and CCQi(t).
A major shortcoming of the Interplex method is that it achieves a constant envelope property on single-carrier signals only. In addition, the Interplex method becomes inefficient when used for combining more than three codes, since the number of code cross-products used for cancellations grows quickly when a larger number of codes are combined. Power efficiency decreases as the number of codes to be combined increases, since a larger number of cross-product terms has to be use for cancellations.
Another way to multiplex modulating codes is a majority logic method disclosed by Spilker and Orr, in an article titled “Code Multiplexing via Majority Logic for GPS Modernization,” prepared for Proc. ION GPS-98, Sep. 15-18, 1998. The majority logic method operates on a principle that at a given time point, the set of chip values (that have values +1 or −1) of an odd number of component codes is inspected and a value of +1 or −1 is selected for the transmission, whichever is assumed by the majority of the codes, as shown in FIG. 1. If the codes share a common chip rate, the operation is done once per chip. When chip rates differ, majority combining is done at their least common multiple.
The majority logic combination of binary signals (or codes) has a good cross-correlation with the component codes, and it also yields a constant envelope signal. However, since the multiplexing is nonlinear, some signal power is lost to intermodulation products and the power efficiency of the method is reduced.
Majority logic combining may be done with uniform or non-uniform weighting. Uniform weighting is accomplished by a voting procedure as described above. In non-uniform weighting, values of some of the codes are given more weight in the voting process and, consequently, these codes end up having higher power in the composite signal.
The majority voting method has, generally, good power efficiency, but it applies only to single carrier signals and the number of codes to be combined has to be odd.
The present invention addresses these shortcomings.